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arXiv · 2508.14353

Non-existence of negative derivations on the higher Nash blowup local algebra

Wágner Badilla-Céspedes·Abel Castorena·Daniel Duarte·Luis Núñez-Betancourt
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Abstract

Let $f\in\mathbb{C}[x_1,\ldots,x_s]$ be a weighted homogeneous polynomial having an isolated singularity and $\mathcal{T}_n(f)$ be its higher Nash blowup local algebra. We show that $\mathcal{T}_n(f)$ does not admit negative weighted derivations for $n\geq2$. This answers affirmatively a conjecture of Hussain-Ma-Yau-Zuo.

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Wágner Badilla-Céspedes, Abel Castorena, Daniel Duarte, Luis Núñez-Betancourt. 2025-08-20. Non-existence of negative derivations on the higher Nash blowup local algebra. https://arxiv.org/abs/2508.14353

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